At the solution of various geometrical tasks quite often it is required to find the area of a triangle or figures which can be presented in the scheme of several triangles. Sometimes the area of this figure is required to be calculated also in life. For determination of the area there are several ways, application of each of which is defined by a type of a triangle and its known parameters.
It is required to you
- - ruler;
- - sheet of paper;
- - calculator.
Instruction
1. Use a so-called formula of Heron for determination of the area of a triangle. For this purpose measure length of the parties of a figure in the beginning, then calculate their sum. Halve the sum of lengths of the parties of a triangle to receive poluperimetr. Substitute the received values in the following formula: S = √ p (p - a) * (p - b) * (p - c), where a, b, c – lengths of the parties of a triangle; p – poluperimetr; √ - the sign of extraction of a square root.
2. If length of one of the parties of a triangle and its height lowered on this party are known multiply length of the party on height, and divide the received result into two.
3. To learn the area of an equilateral triangle, in the beginning build length of its party the second degree. Now increase the received intermediate result by a square root from three. Divide the turned-out number into four.
4. If before you a rectangular triangle, measure by means of a line of length of its legs, that is the parties which adjoin to a right angle. Multiply lengths of legs, and divide the received result into two.
5. If you have data on corner size between two parties of a triangle, and lengths of these parties are known to you, then find the area of a triangle on a formula: St = ½ * A * B * sinα where St is the area of a triangle; A and B – lengths of the parties of a triangle; α - the size of the corner located between these parties.
6. If you know sizes of one of corners (α), length of the party adjoining to it and also size of the second adjacent to this side of angle (β), then for determination of the area square length of the party in the beginning, and then divide the received result into the doubled sum of cotangents of the known corners: St = ½ * A² / (ctg(α) + ctg(β)).